Problem: Simplify the following expression: $x = \dfrac{t^2 + 4t - 5}{t + 5} $
First factor the polynomial in the numerator. $ t^2 + 4t - 5 = (t + 5)(t - 1) $ So we can rewrite the expression as: $x = \dfrac{(t + 5)(t - 1)}{t + 5} $ We can divide the numerator and denominator by $(t + 5)$ on condition that $t \neq -5$ Therefore $x = t - 1; t \neq -5$